I went and reread your original question and realized I didn't really answer the true question. The dealership or used car lot don't have final prices on those vehicles, they have overpricing on new and used cars. If you want to find a cheap used car, goto a dealerships that won't normally sell what you are looking for. Then bargain down from their prices, they will be more willing to go a lower price than other dealers because if they don't sell that Pontiac at their Ford dealership(just an example), they will probably lose more at auction.
Other options besides Private Party sales are sites such as cars.com, carsoup.com, autotrader.com, etc. do an internet search for sites that help owners and dealers to sell cars. It will save time although you will still want to talk to these owners, check out the cars, and do test drives, but you would do the same thing with a dealership anyway. A private party sale usually is the best in terms of getting the best price and knowing where the car came from, but I understand that it really does take a long time to do the entire process.
Also, about Carfax, they are good to know if an insurance-related thing happened such as major crashes, fires, floods, salvage titles, odometer fraud. There is no way they will ever know about a problem that wasn't reported to the insurance company or had police involvement. Just don't forget to use your eyes to spot changes of paint color, misaligned parts, don't forget to look underneath around areas that could be hit, I've seen plenty of cars on lots when I was car shopping where I could see damage when looking under the car where all they did was replace the plastic bumper to make it look nice to sell.
